Pith Number

pith:MHQLRFCI

pith:2008:MHQLRFCIUZSNCE2A22C3EJBGNW

not attested not anchored not stored refs pending

Lectures on Moduli Spaces of Elliptic Curves

Richard Hain

arxiv:0812.1803 v3 · 2008-12-09 · math.AG · math.GT · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHQLRFCIUZSNCE2A22C3EJBGNW}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Conformal Blocks: Vector bundle structures, Sewing, and Factorization

Receipt and verification

First computed	2026-05-18T02:55:39.741442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61e0b89448a664d11340d685b224266d862617b2c2b8a1603a0c06a94bc21273

Aliases

arxiv: 0812.1803 · arxiv_version: 0812.1803v3 · doi: 10.48550/arxiv.0812.1803 · pith_short_12: MHQLRFCIUZSN · pith_short_16: MHQLRFCIUZSNCE2A · pith_short_8: MHQLRFCI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MHQLRFCIUZSNCE2A22C3EJBGNW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 61e0b89448a664d11340d685b224266d862617b2c2b8a1603a0c06a94bc21273

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9791bed5c0394015a7a75dd6b1cc634bc6748cf8e19845db5e0955616fe611d5",
    "cross_cats_sorted": [
      "math.GT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2008-12-09T21:22:30Z",
    "title_canon_sha256": "f6bc4b139c167ef83b51eae598a5164027ab1281a53970e2904fae200afff31d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1803",
    "kind": "arxiv",
    "version": 3
  }
}